The average house has 11 paintings on its walls. Is the mean larger for houses owned by teachers? The data show the results of a survey of 13 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal. 11, 12, 12, 10, 10, 12, 12, 11, 12, 11, 12, 11, 14 What can be concluded at the a= 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer ✓ H₁: ? Select an answer ✓ c. The test statistic?v= (please show your answer to 3 decimal places.) d. The p-value = (Please
The average house has 11 paintings on its walls. Is the mean larger for houses owned by teachers? The data show the results of a survey of 13 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal. 11, 12, 12, 10, 10, 12, 12, 11, 12, 11, 12, 11, 14 What can be concluded at the a= 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer ✓ H₁: ? Select an answer ✓ c. The test statistic?v= (please show your answer to 3 decimal places.) d. The p-value = (Please
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Statistical Analysis of Paintings in Teachers' Homes
#### Research Question:
The average house has 11 paintings on its walls. Is the mean larger for houses owned by teachers? The data show the results of a survey of 13 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.
#### Data Collected:
The number of paintings in each of the 13 teachers' houses:
\[11, 12, 12, 10, 10, 12, 12, 11, 12, 11, 12, 11, 14\]
#### Objective:
Determine if there is statistically significant evidence at the \(\alpha = 0.10\) level of significance to conclude that the mean number of paintings in teachers' houses is greater than the general average of 11 paintings.
#### a. Statistical Test Selection:
For this study, we should use:
\[ \text{Select an answer: (e.g., t-test, Z-test) }\]
#### b. Hypotheses Formulation:
- **Null Hypothesis (\(H_0\))**:
\[
H_0: \mu \leq 11
\]
- **Alternative Hypothesis (\(H_1\))**:
\[
H_1: \mu > 11
\]
Where \(\mu\) is the mean number of paintings in teachers' houses.
#### c. Test Statistic Calculation:
\[
\text{Test statistic:} \quad \text{(Please show your answer to 3 decimal places.)}
\]
#### d. P-value Calculation:
\[
\text{P-value:} \quad \text{(Please show your answer to 4 decimal places.)}
\]
#### e. Conclusion:
Using the p-value, we determine whether to reject the null hypothesis at the 0.10 significance level.
\[
\text{Conclude:} \quad \text{(Select an answer based on the p-value comparison with \(\alpha\))}
\]
This template can guide you through performing a hypothesis test to determine if teachers tend to have more paintings in their homes compared to the general population. Ensure you use the correct statistical formulas and tools for calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53c2050e-df40-4c0a-8720-81a391ef4121%2F9139a869-a692-4b98-863d-36aba3e3ebf6%2Fwp8pw9n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Paintings in Teachers' Homes
#### Research Question:
The average house has 11 paintings on its walls. Is the mean larger for houses owned by teachers? The data show the results of a survey of 13 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.
#### Data Collected:
The number of paintings in each of the 13 teachers' houses:
\[11, 12, 12, 10, 10, 12, 12, 11, 12, 11, 12, 11, 14\]
#### Objective:
Determine if there is statistically significant evidence at the \(\alpha = 0.10\) level of significance to conclude that the mean number of paintings in teachers' houses is greater than the general average of 11 paintings.
#### a. Statistical Test Selection:
For this study, we should use:
\[ \text{Select an answer: (e.g., t-test, Z-test) }\]
#### b. Hypotheses Formulation:
- **Null Hypothesis (\(H_0\))**:
\[
H_0: \mu \leq 11
\]
- **Alternative Hypothesis (\(H_1\))**:
\[
H_1: \mu > 11
\]
Where \(\mu\) is the mean number of paintings in teachers' houses.
#### c. Test Statistic Calculation:
\[
\text{Test statistic:} \quad \text{(Please show your answer to 3 decimal places.)}
\]
#### d. P-value Calculation:
\[
\text{P-value:} \quad \text{(Please show your answer to 4 decimal places.)}
\]
#### e. Conclusion:
Using the p-value, we determine whether to reject the null hypothesis at the 0.10 significance level.
\[
\text{Conclude:} \quad \text{(Select an answer based on the p-value comparison with \(\alpha\))}
\]
This template can guide you through performing a hypothesis test to determine if teachers tend to have more paintings in their homes compared to the general population. Ensure you use the correct statistical formulas and tools for calculations.
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